# General Solution of the Luneberg Lens Problem

@article{Morgan1958GeneralSO, title={General Solution of the Luneberg Lens Problem}, author={Samuel P. Morgan}, journal={Journal of Applied Physics}, year={1958}, volume={29}, pages={1358-1368} }

The general solution is obtained for the index of refraction of a variable‐index, spherical lens which will form perfect geometrical images of the points of two given concentric spheres on each other. One conjugate sphere is assumed to be outside the lens or at its surface, while the other may be either inside, outside, or at the surface. If one of the spheres is of infinite radius, the lens will focus a parallel beam perfectly at a point on the other sphere.It is shown that the index of…

## 168 Citations

A general analysis of geodesic luneberg lenses

- Physics
- 1962

Geodesic lenses have been developed which give a collimated beam diametrically opposite the focal point and at an arbitrary angle relative to the plane of the lens rim. The lenses may have an…

A solution to the complement of the generalized Luneburg lens problem

- PhysicsCommunications Physics
- 2021

Lenses are of interest for the design of directive antennas and multi-optics instruments in the microwave, terahertz and optical domains. Here, we introduce an optical problem defined as the…

Surface-wave luneberg lens antennas

- Physics
- 1960

It is demonstrated that a surface-wave structure having isotropy in the plane of the structure can be operated as a lens. The index of refraction is given for a dielectric slab on a ground plane, a…

Improvements in the computation of refractive-index profiles for the generalized Luneburg lens

- Physics
- 1991

The generalized Luneburg lens problem has been reexamined with the aim of optimizing the methods for computing the Luneburg integral, which determines the refractive-index distribution of spherically…

Electromagnetic scattering from the spherical Luneberg lens

- Physics
- 1994

This study presents a newly developed technique for obtaining the theoretical scattering characteristics of the Luneberg lens. Generally, such calculations are approximated by using multi-layered,…

Microwave heating of a Luneberg lens

- Physics
- 1964

A calculation is made of the maximum steady-state temperature rise due to a small amount of dielectric dissipation in a Luneberg lens which is continuously illuminated by a powerful microwave…

Gradient-index Geodesic Lenses for Integrated Optics: A Uniform Theory

- Physics
- 1988

Abstract A new generation of planar waveguide lenses for integrated-optical circuits is proposed. They have potentially perfect focusing capabilities due to the assumed simultaneous action of the…

Composite modified Luneburg model of human eye lens.

- PhysicsOptics letters
- 2015

A new lens model based on the gradient-index Luneburg lens and composed of two oblate half spheroids of different curvatures is presented to create continuous isoindicial contours and to incorporate curvatures that are similar to those found in a human lens.

Algorithm for lens calculations in the geometrized Maxwell theory

- Computer Science, PhysicsSaratov Fall Meeting
- 2018

The work of the proposed algorithm in the framework of geometrized approach to optics for solving the problem of finding the propagation path of the electromagnetic radiation depending on environmental parameters is demonstrated.

General solution of the non-full-aperture Luneburg lens problem

- Physics
- 1983

The generalized Luneburg lens problem has been redefined to include non-full-aperture lenses, and as a result a new class of solutions has been made possible. A particular solution is obtained for…

## References

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The impossibility of certain desirable luneberg lens modifications

- PhysicsIRE Transactions on Antennas and Propagation
- 1956

THE DIFFICULTY of rapid scanning over the outer surface of a Luneberg lens has led Gutman1 to devise a lens in which the feed moves on a smaller radius. In Gutman's lens the feed horn points toward…

Modified Luneberg Lens

- Physics
- 1954

Spherically symmetric optical instruments, and their desirability for microwaves, are discussed. Application of Hamiltonian optics in analyzing the rays in the Luneberg lens has led to formula of a…